Tan 68 Degrees
The value of tan 68 degrees is 2.4750868. . .. Tan 68 degrees in radians is written as tan (68° × π/180°), i.e., tan (17π/45) or tan (1.186823. . .). In this article, we will discuss the methods to find the value of tan 68 degrees with examples.
- Tan 68° in decimal: 2.4750868. . .
- Tan (-68 degrees): -2.4750868. . .
- Tan 68° in radians: tan (17π/45) or tan (1.1868238 . . .)
What is the Value of Tan 68 Degrees?
The value of tan 68 degrees in decimal is 2.475086853. . .. Tan 68 degrees can also be expressed using the equivalent of the given angle (68 degrees) in radians (1.18682 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 68 degrees = 68° × (π/180°) rad = 17π/45 or 1.1868 . . .
∴ tan 68° = tan(1.1868) = 2.4750868. . .
Explanation:
For tan 68 degrees, the angle 68° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 68° value = 2.4750868. . .
Since the tangent function is a periodic function, we can represent tan 68° as, tan 68 degrees = tan(68° + n × 180°), n ∈ Z.
⇒ tan 68° = tan 248° = tan 428°, and so on.
Note: Since, tangent is an odd function, the value of tan(-68°) = -tan(68°).
Methods to Find Value of Tan 68 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 68° is given as 2.47508. . .. We can find the value of tan 68 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 68 Degrees Using Unit Circle
To find the value of tan 68 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 68° angle with the positive x-axis.
- The tan of 68 degrees equals the y-coordinate(0.9272) divided by x-coordinate(0.3746) of the point of intersection (0.3746, 0.9272) of unit circle and r.
Hence the value of tan 68° = y/x = 2.4751 (approx).
Tan 68° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 68 degrees as:
- sin(68°)/cos(68°)
- ± sin 68°/√(1 - sin²(68°))
- ± √(1 - cos²(68°))/cos 68°
- ± 1/√(cosec²(68°) - 1)
- ± √(sec²(68°) - 1)
- 1/cot 68°
Note: Since 68° lies in the 1st Quadrant, the final value of tan 68° will be positive.
We can use trigonometric identities to represent tan 68° as,
- cot(90° - 68°) = cot 22°
- -cot(90° + 68°) = -cot 158°
- -tan (180° - 68°) = -tan 112°
☛ Also Check:
FAQs on Tan 68 Degrees
What is Tan 68 Degrees?
Tan 68 degrees is the value of tangent trigonometric function for an angle equal to 68 degrees. The value of tan 68° is 2.4751 (approx).
How to Find Tan 68° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 68° can be given in terms of other trigonometric functions as:
- sin(68°)/cos(68°)
- ± sin 68°/√(1 - sin²(68°))
- ± √(1 - cos²(68°))/cos 68°
- ± 1/√(cosec²(68°) - 1)
- ± √(sec²(68°) - 1)
- 1/cot 68°
☛ Also check: trigonometric table
What is the Value of Tan 68 Degrees in Terms of Sin 68°?
Using trigonometric identities, we can write tan 68° in terms of sin 68° as, tan(68°) = sin 68°/√(1 - sin²(68°)) . Here, the value of sin 68° is equal to 0.9272.
What is the Exact Value of tan 68 Degrees?
The exact value of tan 68 degrees can be given accurately up to 8 decimal places as 2.47508685.
How to Find the Value of Tan 68 Degrees?
The value of tan 68 degrees can be calculated by constructing an angle of 68° with the x-axis, and then finding the coordinates of the corresponding point (0.3746, 0.9272) on the unit circle. The value of tan 68° is equal to the y-coordinate(0.9272) divided by the x-coordinate (0.3746). ∴ tan 68° = 2.4751